Time regularity of the densities for the Navier–Stokes equations with noise

Abstract

We prove that the density of the law of any finite-dimensional projection of solutions of the Navier–Stokes equations with noise in dimension three is Holder continuous in time with values in the natural space L 1. When considered with values in Besov spaces, Holder continuity still holds. The Holder exponents correspond, up to arbitrarily small corrections, to the expected, at least with the known regularity, diffusive scaling.